Finite Group Databasebeta

← #13169288

Subgroups — #13169288

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89020C211yesmaximal, characteristic
2C4×#6294C211yesmaximal, characteristic, complemented
3C4×#6289C211yesmaximal, characteristic, complemented
4#11723452C211yesmaximal, characteristic, complemented
5C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
6C3×#63874C211yesmaximal, characteristic, complemented
7C3×#63855C211yesmaximal, characteristic, complemented
8#11722943C212yesmaximal, complemented
9#11722937C212yesmaximal, complemented
10#11722936C212yesmaximal, complemented
11#11722935C212yesmaximal, complemented
12#10594954—31nomaximal
13#10593966—31nomaximal
14#10593965—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6294C2212yes—
19C2×#6293C2211yescharacteristic
20C2×#6292C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6290C2211yescharacteristic
23C2×#6289C2212yes—
24#89020C418yescomplemented
25C2×C3×D3×Dic3C2212yes—
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30#88813C2212yes—
31#88806C2212yes—
32#88804C2212yes—
33Dic3×C3⋊Dic3C2212yes—
34C3×#3724C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×#3828—31no—
40C2×#3798—31no—
41C2×#3798—31no—
42C2×#3798—61no—
43#64081—31no—
44C42×C3⋊D3—31no—
45C3×#926—31no—
46C2×C3×C4×Dic3—31no—
47C3×#872—31no—
48C3×#872—31no—
49C3×#872—31no—
50C3×C42×D3—31no—
51#63952—32no—
52#63952—32no—
53#63904—32no—
54#63902—32no—
55#63894—32no—
56C4×#624—31no—
57C4×#624—31no—
58C4×#624—31no—
59C4×#624—61no—
60#63881—32no—
61#63881—32no—
62#63880—32no—
63#63879—32no—
64C4×D3×Dic3—31no—
65C4×D3×Dic3—31no—
66C4×D3×Dic3D311yescharacteristic, complemented
67#63874—31no—
68#63874—31no—
69#63874—61no—
70#63874D311yescharacteristic, complemented
71#63855D311yescharacteristic, complemented
72#63844—32no—
73#63838—32no—
74#63837—32no—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C4×C3⋊(C3⋊D3)C2×C414yescomplemented
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2312yes—
84C3×C4×C3⋊D3C2×C414yescomplemented
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C32×C4×D3C2×C414yescomplemented
89#6294—24no—
90#6293C2×C414yescomplemented
91#6292C2×C414yescomplemented
92#6291C2×C414yescomplemented
93#6290C2×C414yescomplemented
94#6289—24no—
95C3×D3×Dic3—24no—
96#5522—91no—
97#5522—91no—
98C4×#235—91no—
99C22×C32×C4—31no—
100C2×#638—31no—
101C2×#638—31no—
102#3828—38no—
103C2×C4⋊(C3⋊D3)—31no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—31no—
106C2×C4×C3⋊D3—31no—
107C2×C4×C3⋊D3—32no—
108C2×C4×C3⋊D3—61no—
109C2×C4×C3⋊D3—61no—
110C2×C4×C3⋊D3—61no—
111C2×C4×C3⋊D3—121no—
112C2×C4×C3⋊D3C2×D311yescharacteristic
113C2×#634—31no—
114C22×C3×Dic3—32no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—61no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×#627—31no—
123C2×#627—31no—
124C2×#627—61no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—61no—
130C2×#626—61no—
131C2×#625—31no—
132C2×#625—31no—
133C2×#625—61no—
134C2×#624—32no—
135C2×#624—32no—
136C2×#624—32no—
137C2×#624—62no—
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140C2×D3×Dic3C2×D312yes—
141#3798—38no—
142#3798—38no—
143#3798—68no—
144C32×C42—31no—
145C32×C42—31no—
146#3752—32no—
147#3750—32no—
148C4×C3⋊Dic3—32no—
149C4×C3⋊Dic3C2×D311yescharacteristic
150C4×C3⋊Dic3C2×D311yescharacteristic
151C3×#217—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×C4⋊Dic3—32no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×C4×Dic3—21no—
160C3×C4×Dic3—21no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—32no—
167C3×C4×Dic3—61no—
168C3×C4×Dic3—61no—
169C3×C4×Dic3C2×D311yescharacteristic
170C3×C4×Dic3C2×D311yescharacteristic
171C3×C4×Dic3C2×D311yescharacteristic
172C3×C4×Dic3C2×D311yescharacteristic
173#3724—32no—
174#3724—32no—
175#3724—62no—
176#3724C2×D312yes—
177Dic3⋊Dic3C2×D312yes—
178#3722—32no—
179#3722—32no—
180#3722—62no—
181#3722C2×D312yes—
182(C2×D3)⋊Dic3C2×D312yes—
183Dic32—32no—
184Dic32—32no—
185Dic32—32no—
186Dic32—32no—
187Dic32—32no—
188Dic32—62no—
189Dic32C2×D312yes—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—22no—
192C2×C3⋊(C3⋊D3)C22×C412yes—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3C22×C412yes—
195C2×C32×D3—22no—
196C2×C32×D3C22×C412yes—
197C33×C4C22×C412yes—
198C3⋊(C3⋊Dic3)C22×C412yes—
199C3×C3⋊Dic3—22no—
200C3×C3⋊Dic3C22×C412yes—
201C3×C3⋊Dic3#4114yescomplemented
202C32×Dic3—22no—
203C32×Dic3—22no—
204C32×Dic3C22×C412yes—
205C2×#235—91no—
206C2×#235—91no—
207C2×#235—91no—
208C2×#235—181no—
209C3×#117—91no—
210C3×#117—91no—
211C2×C3×C42—91no—
212C4×#67—92no—
213C4×#67—92no—
214#926—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—91no—
217#893—92no—
218#893—92no—
219#887—92no—
220#887—92no—
221#67⋊C4—92no—
222#67⋊C4—92no—
223#67⋊C4—92no—
224#67⋊C4—92no—
225C4×D12—92no—
226#872—31no—
227#872—31no—
228#872—31no—
229#872—91no—
230#872—91no—
231#872—91no—
232#872—181no—
233C42×D3—31no—
234C42×D3—91no—
235C42×D3—91no—
236C42×D3—91no—
237C42×D3—91no—
238C42×D3—91no—
239C42×D3—181no—
240C4×Dic6—92no—
241C23×C32—31no—
242C22×C3⋊D3—31no—
243C22×C3⋊D3—31no—
244C22×C3⋊D3—31no—
245C22×C3⋊D3—61no—
246C22×C3⋊D3—61no—
247C22×C3⋊D3—61no—
248C22×C3⋊D3—121no—
249C22×C3⋊D3C22×D311yescharacteristic
250C22×C3×D3—21no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—61no—
254C22×C3×D3C22×D311yescharacteristic
255C22×C3×D3C22×D311yescharacteristic
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—31no—
260C2×C32×C4—34no—
261C2×C32×C4—32no—
262C2×C32×C4—32no—
263C2×C32×C4—41no—
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267#638—34no—
268#638—34no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—61no—
273C2×C3⋊Dic3—61no—
274C2×C3⋊Dic3—61no—
275C2×C3⋊Dic3—121no—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D312yes—
279C4⋊(C3⋊D3)—34no—
280C4×C3⋊D3—34no—
281C4×C3⋊D3—34no—
282C4×C3⋊D3—34no—
283C4×C3⋊D3—64no—
284C4×C3⋊D3—64no—
285C4×C3⋊D3—64no—
286C4×C3⋊D3—64no—
287C4×C3⋊D3—124no—
288C4×C3⋊D3C4×D314yescomplemented
289#634—34no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3—64no—
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D312yes—
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D311yescharacteristic
309C3×C4×D3—24no—
310C3×C4×D3—34no—
311C3×C4×D3—34no—
312C3×C4×D3—64no—
313C3×C4×D3—64no—
314C3×C4×D3C4×D314yescomplemented
315C3×C4×D3C4×D314yescomplemented
316#627—34no—
317#627—34no—
318#627—64no—
319#626—34no—
320#626—34no—
321#626—34no—
322#626—34no—
323#626—64no—
324#626—64no—
325#625—34no—
326#625—34no—
327#625—64no—
328#624—64no—
329#624—64no—
330#624—68no—
331#624—64no—
332D3×Dic3—24no—
333D3×Dic3—64no—
334D3×Dic3—64no—
335C4×#41—271noSylow
336C2×C33C23×C411yescharacteristic
337C2×C33C2×#4112yes—
338C3⋊(C3⋊D3)—22no—
339C3×C3⋊D3—22no—
340C32×D3—22no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—92no—
345C22×C3×C4—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—181no—
353C2×#67—181no—
354C22×Dic3—32no—
355C22×Dic3—92no—
356#235—98no—
357#235—98no—
358#235—98no—
359#235—188no—
360C2×D12—91no—
361C2×D12—91no—
362C2×D12—91no—
363C2×D12—181no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—32no—
367C2×C4×D3—61no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—92no—
372C2×C4×D3—92no—
373C2×C4×D3—92no—
374C2×C4×D3—92no—
375C2×C4×D3—92no—
376C2×C4×D3—182no—
377C2×C4×D3—181no—
378C2×C4×D3—181no—
379C2×C4×D3—181no—
380C2×C4×D3—361no—
381C2×C4×D3D3211yescharacteristic
382C2×Dic6—91no—
383C2×Dic6—91no—
384C2×Dic6—91no—
385C2×Dic6—181no—
386C3×C4⋊C4—92no—
387C3×C4⋊C4—92no—
388C3×C22⋊C4—92no—
389C3×C22⋊C4—92no—
390C3×C42—31no—
391C3×C42—31no—
392C3×C42—31no—
393C3×C42—31no—
394C3×C42—61no—
395C3×C42—61no—
396C3×C42—92no—
397C3×C42—91no—
398C3×C42—91no—
399#217—32no—
400(C2×D3)⋊C4—32no—
401(C2×D3)⋊C4—32no—
402(C2×D3)⋊C4—32no—
403(C2×D3)⋊C4—92no—
404(C2×D3)⋊C4—92no—
405(C2×D3)⋊C4—92no—
406(C2×D3)⋊C4—182no—
407C4⋊Dic3—32no—
408Dic3⋊C4—32no—
409Dic3⋊C4—32no—
410Dic3⋊C4—32no—
411Dic3⋊C4—92no—
412Dic3⋊C4—92no—
413Dic3⋊C4—92no—
414Dic3⋊C4—182no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—32no—
420C4×Dic3—32no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—92no—
424C4×Dic3—92no—
425C4×Dic3—92no—
426C4×Dic3—92no—
427C4×Dic3—92no—
428C4×Dic3—92no—
429C4×Dic3—182no—
430C4×Dic3D3211yescharacteristic
431C4×Dic3D3211yescharacteristic
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—32no—
436C22×C32—41no—
437C22×C32—62no—
438C22×C32C23×D311yescharacteristic
439C22×C32C23×D311yescharacteristic
440C22×C32C23×D311yescharacteristic
441C2×C3⋊D3—22no—
442C2×C3⋊D3—32no—
443C2×C3⋊D3—32no—
444C2×C3⋊D3—32no—
445C2×C3⋊D3—62no—
446C2×C3⋊D3—62no—
447C2×C3⋊D3—62no—
448C2×C3⋊D3—62no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—62no—
451C2×C3⋊D3—62no—
452C2×C3⋊D3—122no—
453C2×C3⋊D3—122no—
454C2×C3⋊D3—122no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3C2×C4×D312yes—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—32no—
461C2×C3×D3—32no—
462C2×C3×D3—42no—
463C2×C3×D3—62no—
464C2×C3×D3—62no—
465C2×C3×D3—62no—
466C2×C3×D3—122no—
467C2×C3×D3C2×C4×D312yes—
468C2×C3×D3C2×C4×D312yes—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4—22no—
472C32×C4—32no—
473C32×C4—42no—
474C32×C4—62no—
475C32×C4—62no—
476C32×C4C2×C4×D312yes—
477C32×C4C2×C4×D312yes—
478C32×C4C2×C4×D312yes—
479C3⋊Dic3—22no—
480C3⋊Dic3—32no—
481C3⋊Dic3—32no—
482C3⋊Dic3—32no—
483C3⋊Dic3—62no—
484C3⋊Dic3—62no—
485C3⋊Dic3—62no—
486C3⋊Dic3—122no—
487C3⋊Dic3C2×C4×D312yes—
488C3⋊Dic3#23514yescomplemented
489C3×Dic3—24no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—32no—
496C3×Dic3—32no—
497C3×Dic3—34no—
498C3×Dic3—34no—
499C3×Dic3—42no—
500C3×Dic3—62no—
501C3×Dic3—64no—
502C3×Dic3—62no—
503C3×Dic3—62no—
504C3×Dic3—122no—
505C3×Dic3C2×C4×D312yes—
506C3×Dic3C2×C4×D312yes—
507C2×#41—271no—
508C4×Q8—272no—
509C4×D4—272no—
510C4×D4—272no—
511C4×D4—272no—
512#117—91no—
513#117—91no—
514#117—271no—
515C2×C42—91no—
516C2×C42—271no—
517C2×C42—271no—
518C33C4×#4111yescharacteristic, complemented, Sylow
519C23×C3—31no—
520C23×C3—31no—
521C23×C3—61no—
522C23×C3—91no—
523C22×D3—31no—
524C22×D3—31no—
525C22×D3—61no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—181no—
532C22×D3—361no—
533C22×D3C2×D3211yescharacteristic
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—41no—
546C2×C3×C4—64no—
547C2×C3×C4—62no—
548C2×C3×C4—61no—
549C2×C3×C4—62no—
550C2×C3×C4—92no—
551C2×C3×C4—91no—
552C2×C3×C4—94no—
553C2×C3×C4—92no—
554C2×C3×C4—184no—
555C2×C3×C4C2×D3211yescharacteristic
556C2×C3×C4C2×D3211yescharacteristic
557C2×C3×C4C2×D3211yescharacteristic
558#67—94no—
559#67—94no—
560#67—94no—
561#67—94no—
562#67—94no—
563#67—94no—
564#67—184no—
565#67—184no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—62no—
573C2×Dic3—61no—
574C2×Dic3—62no—
575C2×Dic3—64no—
576C2×Dic3—91no—
577C2×Dic3—91no—
578C2×Dic3—91no—
579C2×Dic3—181no—
580C2×Dic3—181no—
581C2×Dic3—181no—
582C2×Dic3—184no—
583C2×Dic3—361no—
584C2×Dic3C2×D3212yes—
585C2×Dic3C2×D3212yes—
586C2×Dic3C2×D3211yescharacteristic
587D12—94no—
588D12—94no—
589D12—94no—
590D12—184no—
591C4×D3—34no—
592C4×D3—34no—
593C4×D3—64no—
594C4×D3—64no—
595C4×D3—94no—
596C4×D3—94no—
597C4×D3—94no—
598C4×D3—184no—
599C4×D3—184no—
600C4×D3—184no—
601C4×D3—184no—
602C4×D3—184no—
603C4×D3—184no—
604C4×D3—184no—
605C4×D3—188no—
606C4×D3—184no—
607C4×D3—364no—
608C4×D3#62414yescomplemented
609Dic6—94no—
610Dic6—94no—
611Dic6—94no—
612Dic6—184no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—22no—
616C2×C32—22no—
617C2×C32—22no—
618C2×C32—21no—
619C2×C32—41no—
620C2×C32—42no—
621C2×C32—62no—
622C2×C32C22×C4×D311yescharacteristic
623C2×C32C22×C4×D311yescharacteristic
624C2×C32C22×C4×D311yescharacteristic
625C2×C32C2×#23512yes—
626C2×C32D3×#4112yes—
627C2×C32D3×#4112yes—
628C3⋊D3—22no—
629C3⋊D3—62no—
630C3⋊D3—64no—
631C3⋊D3—62no—
632C3⋊D3—62no—
633C3⋊D3—122no—
634C3⋊D3—122no—
635C3⋊D3—124no—
636C3×D3—22no—
637C3×D3—22no—
638C3×D3—42no—
639C3×D3—62no—
640C3×D3—62no—
641C3×D3—122no—
642#41—278no—
643C2×Q8—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C22×C4—31no—
648C22×C4—92no—
649C22×C4—91no—
650C22×C4—272no—
651C22×C4—272no—
652C22×C4—271no—
653C4⋊C4—92no—
654C4⋊C4—92no—
655C4⋊C4—272no—
656C22⋊C4—92no—
657C22⋊C4—92no—
658C22⋊C4—272no—
659C42—31no—
660C42—31no—
661C42—92no—
662C42—91no—
663C42—91no—
664C42—272no—
665C42—272no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—32no—
670C22×C3—32no—
671C22×C3—41no—
672C22×C3—62no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—92no—
676C22×C3—122no—
677C22×C3—182no—
678C22×C3C22×D3211yescharacteristic
679C22×C3C22×D3211yescharacteristic
680C22×C3C22×D3211yescharacteristic
681C2×D3—22no—
682C2×D3—32no—
683C2×D3—32no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—92no—
688C2×D3—92no—
689C2×D3—92no—
690C2×D3—122no—
691C2×D3—182no—
692C2×D3—182no—
693C2×D3—182no—
694C2×D3—184no—
695C2×D3—182no—
696C2×D3—182no—
697C2×D3—182no—
698C2×D3—362no—
699C2×D3—362no—
700C2×D3—362no—
701C2×D3—364no—
702C2×D3C2×#62412yes—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—32no—
707C3×C4—32no—
708C3×C4—42no—
709C3×C4—62no—
710C3×C4—64no—
711C3×C4—62no—
712C3×C4—62no—
713C3×C4—62no—
714C3×C4—62no—
715C3×C4—94no—
716C3×C4—92no—
717C3×C4—122no—
718C3×C4—182no—
719C3×C4C4×D3212yes—
720C3×C4C4×D3212yes—
721C3×C4C2×#62412yes—
722Dic3—22no—
723Dic3—22no—
724Dic3—32no—
725Dic3—32no—
726Dic3—34no—
727Dic3—34no—
728Dic3—62no—
729Dic3—64no—
730Dic3—62no—
731Dic3—62no—
732Dic3—92no—
733Dic3—92no—
734Dic3—92no—
735Dic3—122no—
736Dic3—182no—
737Dic3—182no—
738Dic3—182no—
739Dic3—362no—
740Dic3C2×#62412yes—
741C32—21no—
742C32—21no—
743C32—21no—
744C32—41no—
745C32C4×#23511yescharacteristic, complemented
746C32#552211yescharacteristic, complemented
747C32#552211yescharacteristic, complemented
748C23—31no—
749C23—91no—
750C23—271no—
751Q8—274no—
752D4—274no—
753D4—274no—
754D4—274no—
755C2×C4—31no—
756C2×C4—34no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—92no—
760C2×C4—91no—
761C2×C4—94no—
762C2×C4—92no—
763C2×C4—184no—
764C2×C4—271no—
765C2×C4—274no—
766C2×C4—544no—
767C2×C4—544no—
768C2×C4D3311yescharacteristic
769C2×C3—22no—
770C2×C3—22no—
771C2×C3—22no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—42no—
776C2×C3—41no—
777C2×C3—62no—
778C2×C3—62no—
779C2×C3—122no—
780C2×C3—182no—
781C2×C3C2×C4×D3211yescharacteristic
782C2×C3C2×C4×D3211yescharacteristic
783C2×C3D3×#23512yes—
784C2×C3D3×#23512yes—
785C2×C3#6430612yes—
786C2×C3C22×#62411yescharacteristic
787D3—22no—
788D3—62no—
789D3—62no—
790D3—122no—
791D3—184no—
792D3—182no—
793D3—182no—
794D3—182no—
795D3—362no—
796D3—362no—
797D3—364no—
798C22—32no—
799C22—62no—
800C22—92no—
801C22—182no—
802C22—272no—
803C22—542no—
804C22C2×D3311yescharacteristic
805C4—32no—
806C4—62no—
807C4—62no—
808C4—94no—
809C4—92no—
810C4—182no—
811C4—272no—
812C4D3×#62412yes—
813C3—21no—
814C3—21no—
815C3—21no—
816C3—41no—
817C3#1059396511yescharacteristic, complemented
818C3#1059396611yescharacteristic, complemented
819C3#1059495411yescharacteristic, complemented
820C2—62no—
821C2—182no—
822C2—542no—
823C2#1172438712yes—
824C2C2×D3×#62411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D33
commutatorC2×C33C23×C4
FrattiniC22C2×D33
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89020C2
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×#6294C2semidirect
3. C4×#6289C2semidirect
4. #11723452C2semidirect
5. C3×C4×D3×Dic3C2semidirect
6. C3×#63874C2semidirect
7. C3×#63855C2semidirect
8. #11722943C2semidirect
9. #11722937C2semidirect
10. #11722936C2semidirect
11. #11722935C2semidirect
24. #89020C4semidirect
66. C4×D3×Dic3D3semidirect
70. #63874D3semidirect
71. #63855D3semidirect
80. C4×C3⋊(C3⋊D3)C2×C4semidirect
84. C3×C4×C3⋊D3C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
90. #6293C2×C4semidirect
91. #6292C2×C4semidirect
92. #6291C2×C4semidirect
93. #6290C2×C4semidirect
201. C3×C3⋊Dic3#41semidirect
288. C4×C3⋊D3C4×D3semidirect
314. C3×C4×D3C4×D3semidirect
315. C3×C4×D3C4×D3semidirect
488. C3⋊Dic3#235semidirect
518. C33C4×#41semidirect
608. C4×D3#624semidirect
745. C32C4×#235semidirect
746. C32#5522semidirect
747. C32#5522semidirect
817. C3#10593965semidirect
818. C3#10593966semidirect
819. C3#10594954semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#890202
C4×#62942
C4×#62892
#117234522
C3×C4×D3×Dic32
C3×#638742
C3×#638552
#117229432
#117229372
#117229362
#117229352
#105949543
#105939663
#105939653